precision mathematics and approximation mathematics the conceptual and educational role of their comparison

The relationship between applied and pure mathematics is of utmost concern for Klein. Examples from Volume III of his "Elementarmathematik" illustrate how, starting from an intuitive and sometimes practical approach, Klein develops abstract concepts working in rich "mathematical environments". The examples concern the concept of empirical function and its comparison with an idealised curve, point sets obtained through circular inversion that lead to compare rational numbers and real numbers, and the "continuous" transformation of curves with the help of a point moving in space

Cytokine Production but Lack of Proliferation in Peripheral Blood Mononuclear Cells from Chronic Chagas' Disease Cardiomyopathy Patients in Response to T. cruzi Ribosomal P Proteins

Background:Trypanosoma cruzi ribosomal P proteins, P2β and P0, induce high levels of antibodies in patients with chronic Chagas' disease Cardiomyopathy (CCC). It is well known that these antibodies alter the beating rate of cardiomyocytes and provoke apoptosis by their interaction with β1-adrenergic and M2-muscarinic cardiac receptors. Based on these findings, we decided to study the cellular immune response to these proteins in CCC patients compared to non-infected individuals.Methodology/Principal findings:We evaluated proliferation, presence of surface activation markers and cytokine production in peripheral blood mononuclear cells (PBMC) stimulated with P2β, the C-terminal portion of P0 (CP0) proteins and T. cruzi lysate from CCC patients predominantly infected with TcVI lineage. PBMC from CCC patients cultured with P2β or CP0 proteins, failed to proliferate and express CD25 and HLA-DR on T cell populations. However, multiplex cytokine assays showed that these antigens triggered higher secretion of IL-10, TNF-α and GM-CSF by PBMC as well as both CD4+ and CD8+ T cells subsets of CCC subjects. Upon T. cruzi lysate stimulation, PBMC from CCC patients not only proliferated but also became activated within the context of Th1 response. Interestingly, T. cruzi lysate was also able to induce the secretion of GM-CSF by CD4+ or CD8+ T cells.Conclusions/Significance:Our results showed that although the lack of PBMC proliferation in CCC patients in response to ribosomal P proteins, the detection of IL-10, TNF-α and GM-CSF suggests that specific T cells could have both immunoregulatory and pro-inflammatory potential, which might modulate the immune response in Chagas' disease. Furthermore, it was possible to demonstrate for the first time that GM-CSF was produced by PBMC of CCC patients in response not only to recombinant ribosomal P proteins but also to parasite lysate, suggesting the value of this cytokine to evaluate T cells responses in T. cruzi infection.Fil: Longhi, Silvia Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Investigaciones en Ingeniería Genética y Biología Molecular "Dr. Héctor N. Torres"; Argentina. Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica; ArgentinaFil: Atienza, Augusto. Gobierno de la Ciudad de Buenos Aires. Hospital General de Agudos "Ramos Mejía"; ArgentinaFil: Perez Prados, Graciela. Gobierno de la Ciudad de Buenos Aires. Hospital General de Agudos "Juan A. Fernández"; ArgentinaFil: Buying, Alcinette. Torrey Pines Institute for Molecular Studies; Estados UnidosFil: Balouz, Virginia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Biotecnológicas. Universidad Nacional de San Martín. Instituto de Investigaciones Biotecnológicas; ArgentinaFil: Buscaglia, Carlos Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Biotecnológicas. Universidad Nacional de San Martín. Instituto de Investigaciones Biotecnológicas; ArgentinaFil: Santos, Radleigh. Torrey Pines Institute for Molecular Studies; Estados UnidosFil: Tasso, Laura Mónica. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Investigaciones en Ingeniería Genética y Biología Molecular "Dr. Héctor N. Torres"; ArgentinaFil: Bonato, Ricardo. Gobierno de la Ciudad de Buenos Aires. Hospital General de Agudos "Ramos Mejía"; ArgentinaFil: Chiale, Pablo. Gobierno de la Ciudad de Buenos Aires. Hospital General de Agudos "Ramos Mejía"; ArgentinaFil: Pinilla, Clemencia. Torrey Pines Institute for Molecular Studies; Estados UnidosFil: Judkowski, Valeria A.. Torrey Pines Institute for Molecular Studies; Estados UnidosFil: Gomez, Karina Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Investigaciones en Ingeniería Genética y Biología Molecular "Dr. Héctor N. Torres"; Argentina. Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica; Argentin

A mathematical model of mitochondrial swelling

<p>Abstract</p> <p>Background</p> <p>The <it>permeabilization </it>of mitochondrial membranes is a decisive event in apoptosis or necrosis culminating in cell death. One fundamental mechanism by which such permeabilization events occur is the calcium-induced mitochondrial permeability transition. Upon Ca²⁺-uptake into mitochondria an increase in inner membrane permeability occurs by a yet unclear mechanism. This leads to a net water influx in the mitochondrial matrix, mitochondrial swelling, and finally the rupture of the outer membrane. Although already described more than thirty years ago, many unsolved questions surround this important biological phenomenon. Importantly, theoretical modeling of the mitochondrial permeability transition has only started recently and the existing mathematical models fail to characterize the swelling process throughout the whole time range.</p> <p>Results</p> <p>We propose here a new mathematical approach to the mitochondrial permeability transition introducing a specific delay equation and resulting in an optimized representation of mitochondrial swelling. Our new model is in accordance with the experimentally determined course of volume increase throughout the whole swelling process, including its initial lag phase as well as its termination. From this new model biological consequences can be deduced, such as the confirmation of a positive feedback of mitochondrial swelling which linearly depends on the Ca²⁺-concentration, or a negative exponential dependence of the average swelling time on the Ca²⁺-concentration. Finally, our model can show an initial shrinking phase of mitochondria, which is often observed experimentally before the actual swelling starts.</p> <p>Conclusions</p> <p>We present a model of the mitochondrial swelling kinetics. This model may be adapted and extended to diverse other inducing/inhibiting conditions or to mitochondria from other biological sources and thus may benefit a better understanding of the mitochondrial permeability transition.</p

the italian didactic tradition

Starting with a historic overview highlighting the increasing interest and involvement of the community of mathematicians in educational issues, the chapter outlines some of the crucial features that shaped Italian didactics and, more specifically, the emergence of research studies on mathematics education. Some of these features are related to local conditions, for instance, the high degree of freedom left to the teacher in the design and realization of didactic interventions. The specificity of the Italian case can also be highlighted through a comparison with the reality of other countries. The fruitfulness of this comparison is presented by reporting on collective and personal collaboration experiences between the French and Italian research communities. A final contribution, coming from East Asia, puts the Italian tradition under the lens of a completely new eye, and invites reflection upon historical and institutional aspects of the Italian tradition

The dominant Anopheles vectors of human malaria in Africa, Europe and the Middle East: occurrence data, distribution maps and bionomic précis

<p>Abstract</p> <p>Background</p> <p>This is the second in a series of three articles documenting the geographical distribution of 41 dominant vector species (DVS) of human malaria. The first paper addressed the DVS of the Americas and the third will consider those of the Asian Pacific Region. Here, the DVS of Africa, Europe and the Middle East are discussed. The continent of Africa experiences the bulk of the global malaria burden due in part to the presence of the <it>An. gambiae </it>complex. <it>Anopheles gambiae </it>is one of four DVS within the <it>An. gambiae </it>complex, the others being <it>An. arabiensis </it>and the coastal <it>An. merus </it>and <it>An. melas</it>. There are a further three, highly anthropophilic DVS in Africa, <it>An. funestus</it>, <it>An. moucheti </it>and <it>An. nili</it>. Conversely, across Europe and the Middle East, malaria transmission is low and frequently absent, despite the presence of six DVS. To help control malaria in Africa and the Middle East, or to identify the risk of its re-emergence in Europe, the contemporary distribution and bionomics of the relevant DVS are needed.</p> <p>Results</p> <p>A contemporary database of occurrence data, compiled from the formal literature and other relevant resources, resulted in the collation of information for seven DVS from 44 countries in Africa containing 4234 geo-referenced, independent sites. In Europe and the Middle East, six DVS were identified from 2784 geo-referenced sites across 49 countries. These occurrence data were combined with expert opinion ranges and a suite of environmental and climatic variables of relevance to anopheline ecology to produce predictive distribution maps using the Boosted Regression Tree (BRT) method.</p> <p>Conclusions</p> <p>The predicted geographic extent for the following DVS (or species/suspected species complex*) is provided for Africa: <it>Anopheles </it>(<it>Cellia</it>) <it>arabiensis</it>, <it>An. </it>(<it>Cel.</it>) <it>funestus*</it>, <it>An. </it>(<it>Cel.</it>) <it>gambiae</it>, <it>An. </it>(<it>Cel.</it>) <it>melas</it>, <it>An. </it>(<it>Cel.</it>) <it>merus</it>, <it>An. </it>(<it>Cel.</it>) <it>moucheti </it>and <it>An. </it>(<it>Cel.</it>) <it>nili*</it>, and in the European and Middle Eastern Region: <it>An. </it>(<it>Anopheles</it>) <it>atroparvus</it>, <it>An. </it>(<it>Ano.</it>) <it>labranchiae</it>, <it>An. </it>(<it>Ano.</it>) <it>messeae</it>, <it>An. </it>(<it>Ano.</it>) <it>sacharovi</it>, <it>An. </it>(<it>Cel.</it>) <it>sergentii </it>and <it>An. </it>(<it>Cel.</it>) <it>superpictus*</it>. These maps are presented alongside a bionomics summary for each species relevant to its control.</p

Neuroprotection by adenosine in the brain: From A1 receptor activation to A2A receptor blockade

Adenosine is a neuromodulator that operates via the most abundant inhibitory adenosine A1 receptors (A1Rs) and the less abundant, but widespread, facilitatory A2ARs. It is commonly assumed that A1Rs play a key role in neuroprotection since they decrease glutamate release and hyperpolarize neurons. In fact, A1R activation at the onset of neuronal injury attenuates brain damage, whereas its blockade exacerbates damage in adult animals. However, there is a down-regulation of central A1Rs in chronic noxious situations. In contrast, A2ARs are up-regulated in noxious brain conditions and their blockade confers robust brain neuroprotection in adult animals. The brain neuroprotective effect of A2AR antagonists is maintained in chronic noxious brain conditions without observable peripheral effects, thus justifying the interest of A2AR antagonists as novel protective agents in neurodegenerative diseases such as Parkinson’s and Alzheimer’s disease, ischemic brain damage and epilepsy. The greater interest of A2AR blockade compared to A1R activation does not mean that A1R activation is irrelevant for a neuroprotective strategy. In fact, it is proposed that coupling A2AR antagonists with strategies aimed at bursting the levels of extracellular adenosine (by inhibiting adenosine kinase) to activate A1Rs might constitute the more robust brain neuroprotective strategy based on the adenosine neuromodulatory system. This strategy should be useful in adult animals and especially in the elderly (where brain pathologies are prevalent) but is not valid for fetus or newborns where the impact of adenosine receptors on brain damage is different

Antiinflammatory Therapy with Canakinumab for Atherosclerotic Disease

Background: Experimental and clinical data suggest that reducing inflammation without affecting lipid levels may reduce the risk of cardiovascular disease. Yet, the inflammatory hypothesis of atherothrombosis has remained unproved. Methods: We conducted a randomized, double-blind trial of canakinumab, a therapeutic monoclonal antibody targeting interleukin-1β, involving 10,061 patients with previous myocardial infarction and a high-sensitivity C-reactive protein level of 2 mg or more per liter. The trial compared three doses of canakinumab (50 mg, 150 mg, and 300 mg, administered subcutaneously every 3 months) with placebo. The primary efficacy end point was nonfatal myocardial infarction, nonfatal stroke, or cardiovascular death. RESULTS: At 48 months, the median reduction from baseline in the high-sensitivity C-reactive protein level was 26 percentage points greater in the group that received the 50-mg dose of canakinumab, 37 percentage points greater in the 150-mg group, and 41 percentage points greater in the 300-mg group than in the placebo group. Canakinumab did not reduce lipid levels from baseline. At a median follow-up of 3.7 years, the incidence rate for the primary end point was 4.50 events per 100 person-years in the placebo group, 4.11 events per 100 person-years in the 50-mg group, 3.86 events per 100 person-years in the 150-mg group, and 3.90 events per 100 person-years in the 300-mg group. The hazard ratios as compared with placebo were as follows: in the 50-mg group, 0.93 (95% confidence interval [CI], 0.80 to 1.07; P = 0.30); in the 150-mg group, 0.85 (95% CI, 0.74 to 0.98; P = 0.021); and in the 300-mg group, 0.86 (95% CI, 0.75 to 0.99; P = 0.031). The 150-mg dose, but not the other doses, met the prespecified multiplicity-adjusted threshold for statistical significance for the primary end point and the secondary end point that additionally included hospitalization for unstable angina that led to urgent revascularization (hazard ratio vs. placebo, 0.83; 95% CI, 0.73 to 0.95; P = 0.005). Canakinumab was associated with a higher incidence of fatal infection than was placebo. There was no significant difference in all-cause mortality (hazard ratio for all canakinumab doses vs. placebo, 0.94; 95% CI, 0.83 to 1.06; P = 0.31). Conclusions: Antiinflammatory therapy targeting the interleukin-1β innate immunity pathway with canakinumab at a dose of 150 mg every 3 months led to a significantly lower rate of recurrent cardiovascular events than placebo, independent of lipid-level lowering. (Funded by Novartis; CANTOS ClinicalTrials.gov number, NCT01327846.